An Approximate Analytical Solution of Vibration Problem for Imperfect FGM Shallow Shells with Time Dependent Thickness under Static Loading

Abstract

This paper deals with research of nonlinear vibration of imperfect shallow shells made of functionally-graded materials (FGM) under static and dynamic loadings. The material properties are changing in the thickness direction according to the given power law distribution and the non-linear strain-displacement relationships based on the von Karman theory for moderately large normal deflections. Initial nonlinear system of differential equations transforms to singular ordinary differential equations with variable in time coefficients, which is solved by hybrid perturbation and WKB- Galerkin methods in three steps. Comparison of numerical integration of initial equation and asproximate analytical solutions are given.